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intagrate x 5 /2 dx=alog( x k ) x 7/6 +x 6 (1+x k )

 intagrate      x5/2     dx=alog( xk)


         x7/6+x6                (1+xk)

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans: 5/2
I = \int \frac{x^{5/2}}{x^{6}+x^{7/2}}dx
t = \sqrt{x}
dt = \frac{1}{2\sqrt{x}}dx
I = 2\int \frac{1}{t(t^{5}+1)}dt
s = t^{5}
ds = 5t^{4}dt
I = \frac{2}{5}\int \frac{1}{s(s+1)}ds
I =\frac{2}{5}log(\frac{s}{s+1}) +constant
I =\frac{2}{5}log(\frac{t^{5}}{t^{5}+1}) +constant
I =\frac{2}{5}log(\frac{x^{5/2}}{x^{5/2}+1}) +constant
k = 5/2
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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